We present an efficient method for modeling 3-D doubly periodic structures over a wide frequency range based on hybrid finite element/boundary integral (FEBI) methods. The 3-D periodic structures can be represented as non-orthogonal lattices composed of inhomogeneous bianisotropic media with arbitrary metallic patches. Triangular prismatic volume elements were utilized to mesh the unit cell, which provided a great deal of flexibility in modeling complex planar geometries of arbitrary shape. The adaptive integral method (AIM) was applied to speed up the calculation of the matrix-vector product for the BI part within the iterative solver. Furthermore, a model-based parameter estimation (MBPE) technique was proposed for the wide-band interpolation of sparse impedance matrix elements in the BI portion for near field components that were used in the AIM. The accuracy and efficiency of the proposed algorithm is demonstrated by the presented numerical results. To demonstrate the flexibility of the proposed method in modeling arbitrarily shaped elements of frequency selective surfaces (FSS), we included simulation results for an FSS with a non-orthogonal lattice and two elliptical shaped patches embedded in bianisotropic media.